The typical Populist critique of society is that it is run by elites for their own benefit. It argues that the wealthy people in a society are the ones who typically benefit from things that the government does while the "common people" are left to suffer.
The Populists of 1892 (the People's Party) believed very much in this idea. They called for various government actions that would curb the wealthy for the benefit of the common people. For example, they wanted government ownership of utility companies and railroads so that wealthy businessmen could not use their control of such necessities to squeeze the poor. They also called for a purer democracy with, for example, direct election of Senators so that the more numerous common people could influence the government more than the elites.
Overall, then, their critique of society was that it was controlled by wealthy elites and run for the benefit of those elites.